Problem: Which of the following numbers is a multiple of 11? ${43,44,92,106,119}$
Answer: The multiples of $11$ are $11$ $22$ $33$ $44$ ..... In general, any number that leaves no remainder when divided by $11$ is considered a multiple of $11$ We can start by dividing each of our answer choices by $11$ $43 \div 11 = 3\text{ R }10$ $44 \div 11 = 4$ $92 \div 11 = 8\text{ R }4$ $106 \div 11 = 9\text{ R }7$ $119 \div 11 = 10\text{ R }9$ The only answer choice that leaves no remainder after the division is $44$ $ 4$ $11$ $44$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $44$ $44 = 2\times2\times11 11 = 11$ Therefore the only multiple of $11$ out of our choices is $44$. We can say that $44$ is divisible by $11$.